Classification and reconstruction for single-pixel imaging with classical and quantum neural networks

TL;DR

The paper tackles reconstructing and classifying high-dimensional images from a small number of single-pixel measurements using Hadamard patterns, comparing classical fully connected neural networks with parameterized quantum circuits. It demonstrates that a classical classifier achieves about 96% accuracy while a quantum classifier reaches about 95% accuracy after training, whereas reconstruction quality favors the classical model (SSIM ≈ 0.76) over the quantum one (SSIM ≈ 0.25). The study also shows that using 64 measurements (roughly 6% of the full Hadamard set) is near-optimal for classification, but quantum reconstruction remains a substantial challenge within the current experimental configuration. Overall, the results illustrate the potential of quantum ML in single-pixel imaging and highlight the need for advances in data encoding, qubit counts, and hardware to realize comparable performance in reconstruction tasks.

Abstract

Single-pixel cameras are effective solution for imaging outside the visible spectrum where traditional CMOS/CCD cameras have challenges. Combined with machine learning, they can analyze images quickly enough for practical applications. Solving the problem of high-dimensional single-pixel visualization can potentially be accelerated using quantum machine learning, thereby expanding the range of practical problems. In this work we simulated a single-pixel imaging experiment using Hadamard basis patterns, where images from the MNIST handwritten digit dataset were used as objects. There were selected 64 measurements with maximum variance (6% of the number of pixels in the image). We created algorithms for classifying and reconstruction images based on these measurements using classical fully connected neural networks and parameterized quantum circuits. Classical and quantum classifiers showed accuracies of 96% and 95% respectively after 6 training epochs, which is quite competitive result. Image reconstruction was also demonstrated using classical and quantum neural networks after 10 training epochs, the structural similarity index measure values were 0.76 and 0.25, respectively, which indicates that the problem in such a formulation turned out to be too difficult for quantum neural networks in such a configuration for now.

Figures (7)

• Figure 1: Example of several Hadamard patterns $H_n ^{(i)}$) (rows of matrix $H_n$ resized to $n \times n$)
• Figure 2: Dependence of test set (a) - accuracy of classification, (b) - mean squared error of image reconstruction, - on the number of measurements in the Hadamard basis in the input layer of neural network
• Figure 3: One layer structure of parameterized quantum circuit
• Figure 4: Validation accuracy while training various classification neural networks, quantum with different number of layers (1, 3, 6, 10, 15, 30) and classical
• Figure 5: Validation mean squared error while training various reconstruction neural networks, quantum with different number of layers (10, 20, 30, 40) and classical